Conducting wires generate electromagnetic fields and have coupling fields to other components and circuits. These fields can lead to malfunction or permanently damages. It is important to be able to quantify the emission of fields. In this study, the radiation of fields from a wire interconnects has been investigated. The modeling for emission was created via Java and Matlab GUI applets. This work presents a model to determine radiation of transmission line with and without ground. The effect of ground is crucial for near field radiation. There exist many theoretical explanations about radiation of fields. The pattern of radiated fields is indicated as the near field and far field radiation. Understanding the radiation phenomena, the simulation of radiation pattern and the examples of numerical computation have been shown with and without ground plane. Its configuration and presence of conducting plane are also kept in mind.
The transmission line, shown in Figure 1, consists of a pair of parallel conducting wires with constant separation. According to this transmission line without ground plane, the radiation from each of the opposite currents are assumed the same and are summed. The circuit length L should be large, and the circuit width w is small to have limited radiation. The radiated electric field of the circuit in the xy plane is [16]
where Z0 is the characteristic impedance of free space, f is frequency, r is the observation distance, c is the speed of light, |I| is the peak amplitude of the current, vp is the propagation velocity, θ is the elevation angle, and ϕ is the azimuth angle. In the circuit, VS is the voltage source, RL and RS are load resistance and source resistance, respectively. Considering the ground plane, the radiating images of currents are taken into consideration. h is the distance between the transmission line and the ground. There are two situations. If the transmission line is parallel to the ground, the image currents are in the same directions. If the transmission line is perpendicular to the ground, the image currents are in opposite directions. The radiated field over the ground is the sum of the circuit radiation and its image.
From theory, computer code has been written to simulate and determine radiation and is packaged as an applet. Field components are presented in Cartesian and polar coordinates.
A transmission line without ground plane, with wire diameter d = 0.5 mm, w = 50 mm, f = 1 MHz, L = 1 m, r = 1 m, RL = 50 Ω, RS = 50Ω and VS = 1 V is computed using the applet composed. The results can be compared with [17–18]. Figures 2 and 3 show the simulation results for polar coordinates without and with ground, respectively. It is seen that Eϕ and Ex components do not exist for ϕ =90◦. All the other components are plotted and compared with other coordinates easily. The second model is done for the transmission line with ground plane with h = 5 mm to show the ground effect.
Figure 2. The (a) Polar and (b) Cartesian field components for ϕ =90°
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